Emilia and Jessica are hosting events that are catered by the same company. Emilia plans to have 96 adults and 42 children attend, so the total projected cost of her meals is $3,336. Jessica has 79 adults and 74 children on her guest list, so she will pay the caterer $3,534. How much does the caterer charge for each meal?
First find the cost per adult's meal by subtracting the cost of the children's meals from the total cost for Emilia's meals: $3,336 - $42/child * $3360/child = $3360.
Then divide that cost by the number of adults to find the cost per adult: $3360 / 96 people = $<<3360/96=35>>35/person.
Then find the cost per child's meal in a similar way: $3,534 - $79/adult * $35/adult = $3,534 - $2765 = $769.
Then divide that number by the number of children to find the cost per child: $769 / 74 children = $<<769/74=10.39>>10.39/child. Answer: \boxed{10.39}.